Finite Group Databasebeta

← C13×#33807 #15720146

Subgroups — C13×#33807 #15720146

Order 3328.

466 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3176C211yesmaximal, characteristic
2C13×#3164C211yesmaximal, characteristic, complemented
3C13×#2255C211yesmaximal, characteristic, complemented
4C13×#2253C211yesmaximal, characteristic, complemented
5C13×#2244C211yesmaximal, characteristic, complemented
6C13×#2240C211yesmaximal, characteristic, complemented
7C13×#2234C211yesmaximal, characteristic, complemented
8C13×#2234C211yesmaximal, characteristic, complemented
9C13×#2233C211yesmaximal, characteristic, complemented
10C13×#2232C211yesmaximal, characteristic, complemented
11C13×#2228C211yesmaximal, characteristic, complemented
12C13×#2228C211yesmaximal, characteristic, complemented
13C13×#2226C211yesmaximal, characteristic, complemented
14C13×#2224C211yesmaximal, characteristic, complemented
15C13×#2164C211yesmaximal, characteristic, complemented
16C13×#544—21no—
17C13×#540—21no—
18C13×#501—21no—
19C13×#501—21no—
20C13×#500C2211yescharacteristic
21C13×#500C2211yescharacteristic
22C13×#499C2211yescharacteristic
23C13×#499C2211yescharacteristic
24C13×#499C2211yescharacteristic
25C13×#493C2211yescharacteristic
26C13×#490—21no—
27C13×#469—21no—
28C13×#466C2211yescharacteristic
29C13×#466C2211yescharacteristic
30C13×#442—21no—
31C4×C13×D8C2211yescharacteristic
32C4×C13×D8C2211yescharacteristic
33C13×#428—21no—
34C13×#427C2211yescharacteristic
35C2×C13×#107C2211yescharacteristic
36C13×#405C2211yescharacteristic
37C13×#367C2211yescharacteristic
38C13×#367C2211yescharacteristic
39C13×#367C2211yescharacteristic
40C13×#367C2211yescharacteristic
41C13×#366C2211yescharacteristic
42C13×#366C2211yescharacteristic
43C13×#366C2211yescharacteristic
44C13×#366C2211yescharacteristic
45C13×C4⋊C16C2211yescharacteristic
46C13×C4⋊C16C2211yescharacteristic
47C13×#357C2211yescharacteristic
48C13×#357C2211yescharacteristic
49C13×#357C2211yescharacteristic
50C13×#357C2211yescharacteristic
51C13×#357C2211yescharacteristic
52C13×#357C2211yescharacteristic
53C13×#357C2211yescharacteristic
54C13×#357C2211yescharacteristic
55C13×C22⋊C16C2211yescharacteristic
56C13×C22⋊C16C2211yescharacteristic
57C13×#346C2211yescharacteristic
58C4×C13×C16C2211yescharacteristic
59C2×C13×D8—21no—
60C2×C13×D8C2311yescharacteristic
61C2×C13×D8C2311yescharacteristic
62C2×C13×M16D411yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C13×C4⋊Q8—21no—
65C13×C4⋊Q8—21no—
66C13×C4⋊Q8—41no—
67C13×#127—21no—
68C13×#125—21no—
69C13×#125—21no—
70C13×#125—21no—
71C13×#125—41no—
72C13×#123—41no—
73C13×#123—41no—
74C13×C22⋊Q8—41no—
75C13×C22⋊Q8—41no—
76C13×#121—21no—
77C13×#121—21no—
78C13×#121—41no—
79C13×#121—41no—
80C4×D4×C13—21no—
81C4×D4×C13—21no—
82C13×#117—21no—
83C13×#117D411yescharacteristic
84C2×C13×C4⋊C4—21no—
85C2×C13×C16C2311yescharacteristic
86C2×C13×C16C2311yescharacteristic
87C2×C13×C16C2311yescharacteristic
88C2×C13×C16C2311yescharacteristic
89C13×#107—21no—
90C13×#107—21no—
91C13×#107—21no—
92C13×#107C2311yescharacteristic
93C13×#107C2311yescharacteristic
94C13×#107C2311yescharacteristic
95C13×#107C2311yescharacteristic
96C13×#107C2311yescharacteristic
97C13×#107C2311yescharacteristic
98C13×#106—21no—
99C13×#106—21no—
100C13×#106—21no—
101C13×#106—21no—
102C13×#102—21no—
103C13×#102—21no—
104C13×#102—21no—
105C13×#102—21no—
106C13×#97D411yescharacteristic
107C13×#97D411yescharacteristic
108C4×C8×C13C2311yescharacteristic
109C4×C8×C13C2311yescharacteristic
110#33807C1311yesmaximal, characteristic, direct product factor, Sylow
111C2×Q8×C13—41no—
112C2×Q8×C13—41no—
113C2×D4×C13—21no—
114C2×D4×C13—21no—
115C2×D4×C13—41no—
116C2×D4×C13—41no—
117C2×D4×C13—41no—
118C2×D4×C13—41no—
119C22×C4×C13—41no—
120C22×C4×C13—41no—
121C22×C4×C13—41no—
122C22×C4×C13C2×D411yescharacteristic
123C13×D8—21no—
124C13×D8—21no—
125C13×D8—21no—
126C13×D8—21no—
127C13×D8—42no—
128C13×M16—22no—
129C2×C8×C13—21no—
130C2×C8×C13—21no—
131C2×C8×C13C2×D411yescharacteristic
132C2×C8×C13C2×D411yescharacteristic
133C2×C8×C13C2×D411yescharacteristic
134C2×C8×C13C2411yescharacteristic
135C13×C4⋊C4—21no—
136C13×C4⋊C4—21no—
137C13×C4⋊C4—21no—
138C13×C4⋊C4—21no—
139C13×C4⋊C4—21no—
140C13×C4⋊C4—21no—
141C13×C4⋊C4—41no—
142C13×C4⋊C4—41no—
143C13×C4⋊C4—41no—
144C13×C4⋊C4—41no—
145C13×C4⋊C4—41no—
146C13×C4⋊C4—41no—
147C13×C4⋊C4—41no—
148C13×C4⋊C4—41no—
149C13×C4⋊C4—41no—
150C13×C4⋊C4D811yescharacteristic
151C13×C4⋊C4D811yescharacteristic
152C13×C22⋊C4—41no—
153C13×C22⋊C4—41no—
154C13×C22⋊C4—41no—
155C13×C22⋊C4—41no—
156C13×C22⋊C4—41no—
157C13×C22⋊C4D811yescharacteristic
158C13×C22⋊C4D811yescharacteristic
159C42×C13—41no—
160C42×C13C2×D411yescharacteristic
161C42×C13C2×D411yescharacteristic
162C13×C16—21no—
163C13×C16—21no—
164C13×C16—21no—
165C13×C16—21no—
166#3176C2×C1311yescharacteristic
167#3164C2×C1311yescharacteristic, complemented
168#2255C2×C1311yescharacteristic, complemented
169#2253C2×C1311yescharacteristic, complemented
170#2244C2×C1311yescharacteristic, complemented
171#2240C2×C1311yescharacteristic, complemented
172#2234C2×C1311yescharacteristic, complemented
173#2234C2×C1311yescharacteristic, complemented
174#2233C2×C1311yescharacteristic, complemented
175#2232C2×C1311yescharacteristic, complemented
176#2228C2×C1311yescharacteristic, complemented
177#2228C2×C1311yescharacteristic, complemented
178#2226C2×C1311yescharacteristic, complemented
179#2224C2×C1311yescharacteristic, complemented
180#2164C2×C1311yescharacteristic, complemented
181C23×C13—41no—
182C23×C13—41no—
183C23×C13C2×D811yescharacteristic
184Q8×C13—161no—
185Q8×C13—161no—
186D4×C13—41no—
187D4×C13—41no—
188D4×C13—41no—
189D4×C13—41no—
190D4×C13—161no—
191D4×C13—161no—
192D4×C13—161no—
193D4×C13—161no—
194C2×C4×C13—21no—
195C2×C4×C13—21no—
196C2×C4×C13—41no—
197C2×C4×C13—41no—
198C2×C4×C13—41no—
199C2×C4×C13—41no—
200C2×C4×C13—41no—
201C2×C4×C13—41no—
202C2×C4×C13—161no—
203C2×C4×C13—161no—
204C2×C4×C13—161no—
205C2×C4×C13C2×D811yescharacteristic
206C2×C4×C13C2×D811yescharacteristic
207C2×C4×C13C2×D811yescharacteristic
208C2×C4×C13C2×D811yescharacteristic
209C2×C4×C13C2×D811yescharacteristic
210C2×C4×C13C22×D411yescharacteristic
211C8×C13—21no—
212C8×C13—21no—
213C8×C13#13712yes—
214C8×C132−1+411yescharacteristic
215C8×C132−1+411yescharacteristic
216#544—21no—
217#540—21no—
218#501—21no—
219#501—21no—
220#500C22×C1311yescharacteristic
221#500C22×C1311yescharacteristic
222#499C22×C1311yescharacteristic
223#499C22×C1311yescharacteristic
224#499C22×C1311yescharacteristic
225#493C22×C1311yescharacteristic
226#490—21no—
227#469—21no—
228#466C22×C1311yescharacteristic
229#466C22×C1311yescharacteristic
230#442—21no—
231C4×D8C22×C1311yescharacteristic
232C4×D8C22×C1311yescharacteristic
233#428—21no—
234#427C22×C1311yescharacteristic
235C2×#107C22×C1311yescharacteristic
236#405C22×C1311yescharacteristic
237#367C22×C1311yescharacteristic
238#367C22×C1311yescharacteristic
239#367C22×C1311yescharacteristic
240#367C22×C1311yescharacteristic
241#366C22×C1311yescharacteristic
242#366C22×C1311yescharacteristic
243#366C22×C1311yescharacteristic
244#366C22×C1311yescharacteristic
245C4⋊C16C22×C1311yescharacteristic
246C4⋊C16C22×C1311yescharacteristic
247#357C22×C1311yescharacteristic
248#357C22×C1311yescharacteristic
249#357C22×C1311yescharacteristic
250#357C22×C1311yescharacteristic
251#357C22×C1311yescharacteristic
252#357C22×C1311yescharacteristic
253#357C22×C1311yescharacteristic
254#357C22×C1311yescharacteristic
255C22⋊C16C22×C1311yescharacteristic
256C22⋊C16C22×C1311yescharacteristic
257#346C22×C1311yescharacteristic
258C4×C16C22×C1311yescharacteristic
259C22×C13—21no—
260C22×C13—21no—
261C22×C13—21no—
262C22×C13—81no—
263C22×C13—81no—
264C22×C13—81no—
265C22×C13—81no—
266C22×C13—81no—
267C22×C13—81no—
268C22×C13C22×D811yescharacteristic
269C4×C13—21no—
270C4×C13—21no—
271C4×C13—21no—
272C4×C13—21no—
273C4×C13—21no—
274C4×C13—81no—
275C4×C13—81no—
276C4×C13—81no—
277C4×C13—81no—
278C4×C13—81no—
279C4×C13—81no—
280C4×C13#53611yescharacteristic
281C4×C13C2×#13711yescharacteristic
282C2×D8—21no—
283C2×D8C23×C1311yescharacteristic
284C2×D8C23×C1311yescharacteristic
285C2×M16D4×C1311yescharacteristic
286C22×C8C23×C1311yescharacteristic
287C4⋊Q8—21no—
288C4⋊Q8—21no—
289C4⋊Q8—41no—
290#127—21no—
291#125—21no—
292#125—21no—
293#125—21no—
294#125—41no—
295#123—41no—
296#123—41no—
297C22⋊Q8—41no—
298C22⋊Q8—41no—
299#121—21no—
300#121—21no—
301#121—41no—
302#121—41no—
303C4×D4—21no—
304C4×D4—21no—
305#117—21no—
306#117D4×C1311yescharacteristic
307C2×C4⋊C4—21no—
308C2×C16C23×C1311yescharacteristic
309C2×C16C23×C1311yescharacteristic
310C2×C16C23×C1311yescharacteristic
311C2×C16C23×C1311yescharacteristic
312#107—21no—
313#107—21no—
314#107—21no—
315#107C23×C1311yescharacteristic
316#107C23×C1311yescharacteristic
317#107C23×C1311yescharacteristic
318#107C23×C1311yescharacteristic
319#107C23×C1311yescharacteristic
320#107C23×C1311yescharacteristic
321#106—21no—
322#106—21no—
323#106—21no—
324#106—21no—
325#102—21no—
326#102—21no—
327#102—21no—
328#102—21no—
329#97D4×C1311yescharacteristic
330#97D4×C1311yescharacteristic
331C4×C8C23×C1311yescharacteristic
332C4×C8C23×C1311yescharacteristic
333C2×C13—41no—
334C2×C13—161no—
335C2×C13—161no—
336C2×C13#322611yescharacteristic
337C2×C13#341511yescharacteristic
338C2×C13#341611yescharacteristic
339C2×Q8—41no—
340C2×Q8—41no—
341C2×D4—21no—
342C2×D4—21no—
343C2×D4—41no—
344C2×D4—41no—
345C2×D4—41no—
346C2×D4—41no—
347C22×C4—41no—
348C22×C4—41no—
349C22×C4—41no—
350C22×C4C2×D4×C1311yescharacteristic
351D8—21no—
352D8—21no—
353D8—21no—
354D8—21no—
355D8—42no—
356M16—22no—
357C2×C8—21no—
358C2×C8—21no—
359C2×C8C2×D4×C1311yescharacteristic
360C2×C8C2×D4×C1311yescharacteristic
361C2×C8C2×D4×C1311yescharacteristic
362C2×C8C24×C1311yescharacteristic
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4C13×D811yescharacteristic
379C4⋊C4C13×D811yescharacteristic
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4C13×D811yescharacteristic
386C22⋊C4C13×D811yescharacteristic
387C42—41no—
388C42C2×D4×C1311yescharacteristic
389C42C2×D4×C1311yescharacteristic
390C16—21no—
391C16—21no—
392C16—21no—
393C16—21no—
394C13#3380711yescharacteristic, direct product factor, Sylow
395C23—41no—
396C23—41no—
397C23C2×C13×D811yescharacteristic
398Q8—161no—
399Q8—161no—
400D4—41no—
401D4—41no—
402D4—41no—
403D4—41no—
404D4—161no—
405D4—161no—
406D4—161no—
407D4—161no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—161no—
417C2×C4—161no—
418C2×C4—161no—
419C2×C4C2×C13×D811yescharacteristic
420C2×C4C2×C13×D811yescharacteristic
421C2×C4C2×C13×D811yescharacteristic
422C2×C4C2×C13×D811yescharacteristic
423C2×C4C2×C13×D811yescharacteristic
424C2×C4C22×D4×C1311yescharacteristic
425C8—21no—
426C8—21no—
427C8C13×#13712yes—
428C8C13×2−1+411yescharacteristic
429C8C13×2−1+411yescharacteristic
430C22—21no—
431C22—21no—
432C22—21no—
433C22—81no—
434C22—81no—
435C22—81no—
436C22—81no—
437C22—81no—
438C22—81no—
439C22C22×C13×D811yescharacteristic
440C4—21no—
441C4—21no—
442C4—21no—
443C4—21no—
444C4—21no—
445C4—81no—
446C4—81no—
447C4—81no—
448C4—81no—
449C4—81no—
450C4—81no—
451C4C13×#53611yescharacteristic
452C4C2×C13×#13711yescharacteristic
453C2—41no—
454C2—161no—
455C2—161no—
456C2C13×#322611yescharacteristic
457C2C13×#341511yescharacteristic
458C2C13×#341611yescharacteristic
subgroupG/H
center, socleC22×C13C22×D8
commutator, Frattini, cosocleC2×C8C24×C13
prime radicalC13×#3176C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C13×#117 ◁ C13×#405 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C13×#3164C2semidirect
3. C13×#2255C2semidirect
4. C13×#2253C2semidirect
5. C13×#2244C2semidirect
6. C13×#2240C2semidirect
7. C13×#2234C2semidirect
8. C13×#2234C2semidirect
9. C13×#2233C2semidirect
10. C13×#2232C2semidirect
11. C13×#2228C2semidirect
12. C13×#2228C2semidirect
13. C13×#2226C2semidirect
14. C13×#2224C2semidirect
15. C13×#2164C2semidirect
110. #33807C13direct (N × H)
167. #3164C2×C13semidirect
168. #2255C2×C13semidirect
169. #2253C2×C13semidirect
170. #2244C2×C13semidirect
171. #2240C2×C13semidirect
172. #2234C2×C13semidirect
173. #2234C2×C13semidirect
174. #2233C2×C13semidirect
175. #2232C2×C13semidirect
176. #2228C2×C13semidirect
177. #2228C2×C13semidirect
178. #2226C2×C13semidirect
179. #2224C2×C13semidirect
180. #2164C2×C13semidirect
394. C13#33807direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C13×#31762
C13×#31642
C13×#22552
C13×#22532
C13×#22442
C13×#22402
C13×#22342
C13×#22332
C13×#22322
C13×#22282
C13×#22262
C13×#22242
C13×#21642
#3380713